Nearly two-thirds of people believe there will be a 'clash of civilisations' between British Muslims and white Britons in the wake of the murder of a British soldier in Woolwich, a new poll shows.

The number of those who believe such a clash is inevitable has increased by 9% from last year.

There has also been a small increase in the proportion of people who believe British Muslims pose a serious threat to democracy, up to 34% on Thursday and Friday from 30% in November 2012, according to the YouGov survey of 1,839 adults.

The poll will fuel concern of an explosion of race hate, with one interfaith charity reporting a huge increase in anti-Muslim incidents since the murder of soldier Lee Rigby in south-east London on Wednesday.

Faith Matters, which runs a helpline, said they had received 162 calls since the attack, up from a daily average of six.

A number of people have also been charged by police after allegedly offensive messages were posted on social media websites. These include a 22-year-old man from Lincoln, a 28-year-old man from London, a 23-year-old woman from Southsea, and a 19-year-old man from Woking.

The BNP has also announced it will be demonstrating in Woolwich. National organiser Adam Walker claims the brutal murder meant a "line has been drawn in the sand and it signals the beginning of the civil war we have predicted for years".

However the YouGov poll provides evidence that Britain does remain a tolerant country and that the far-right support remains at the margins of society. Nearly two-thirds (63%) believe the vast majority of Muslims are good British citizens, up by 1% from last November.

There has also been an increase from 24% to 33% in the proportion who believe Muslims are compatible with the 'British way of life'. Around two-thirds (65%) said on the whole most people tend to get along well with each other.

One in five respondents said they felt positively about demonstrations being held against last week's terror attacks, and half felt negatively.

However, two-thirds said they felt negatively about such protests led by the BNP or English Defence League (EDL). Asked if they would join the EDL, 84% said they would never do so, although there has been a 9% increase in the proportion of respondents who had heard of the far-right organisation.

Dr Matthew Goodwin of Nottingham university, who commissioned the poll, said: "Compared to last year, when we ran the exact same survey, today people are either just as likely, or more likely, to endorse a series of more positive statements: that Muslims are compatible with the national way of life; are good citizens; make important contributions to society; and share British culture and values.

"In fact, while far right groups were pointing to the murder as evidence that Islam poses a fundamental threat to modern Britain, the percentage of respondents who view Muslims as compatible actually jumped by almost ten points, to 33%.

"Clearly, the numbers remain low, and point to wider challenges facing government, and our local communities. But in the aftermath of events that could well have triggered a more serious backlash, the direction of travel remains positive, and suggests there has not been a sharp spike in prejudice."

The underlining tolerance appears to back up the prime minister's statement last week in which he said the murder of Rigby on a Woolwich street was "not just an attack on Britain, and on the British way of life, it was also a betrayal of Islam and of the Muslim communities who give so much to this country."

On Saturday a demonstration by the EDL in Newcastle was met by a anti-fascist protest, chanting: "Nazi scum, off our streets."

Yvette Cooper, the shadow home secretary, said groups such as the EDL were fuelling division and helping those behind terror attacks. She said: "Anyone who seeks to divide our communities is doing the work of the extremists they say they oppose.

"Mindless acts of violence against any of our communities serve no-one. Some people are trying to use the vile attack in Woolwich as an excuse for more hatred, violence, and extremism. We must not let them.

"The police, security services and all right minded people in this country will do everything they can to make sure any act of violence and intimidation is dealt with robustly and quickly.

"The clear message from the overwhelming majority of British people is 'not in my name'. We stand together against violent extremism, intolerance and hatred – whether it comes from Islamist extremists, the EDL, the BNP, or extremists of any kind."